An Estimation of Distribution Algorithm for Permutation Flow-Shop Scheduling Problem

Abstract

Estimation of distribution algorithms (EDAs) is a subset of evolutionary algorithms widely used in various optimization problems, known for their favorable results. Each generation of EDAs builds a probabilistic model to represent the most promising individuals, and the next generation is created by sampling from this model. The primary challenge in designing such algorithms lies in effectively constructing the probabilistic model. The mutual exclusivity constraint imposes an additional challenge for EDAs to approach permutation-based problems. In this study, we propose a new EDA called Position-Guided Sampling Estimation of Distribution Algorithm (PGS-EDA) specifically designed for permutation-based problems. Unlike conventional approaches, our algorithm focuses on the positions rather than the elements during the sampling phase. We evaluate the performance of our algorithm on the Permutation Flow-shop Scheduling Problem (PFSP). The experiments conducted on various sizes of Taillard instances provide evidence of the effectiveness of our algorithm in addressing the PFSP, particularly for small and medium-sized problems. The comparison results with other EDAs designed to handle permutation problems demonstrate that our PSG-EDA algorithm consistently achieves the lowest Average Relative Percentage Deviation (ARPD) values in 19 out of the 30 instances of sizes 20 and 50 used in the study. These findings validate the superior performance of our algorithm in terms of minimizing the makespan criterion of the PFSP.

Keywords

• estimation of distribution algorithms
• permutation-based problems
• scheduling problems
• evolutionary algorithms